一些关于C4对星的Set Ramsey 数
Some Values of Set Ramsey Numbers forC 4versus Stars
DOI:10.12677/AAM.2024.132082,PDF,下载: 180浏览: 311
作者:熊慧芸：浙江师范大学数学科学学院，浙江 金华
关键词:有限射影平面；极性图；多部图；Set Ramsey数；Finite Projective Plane；Polarity Graph；Multipartite Diagram；Set Ramsey Number
摘要:运用参数坐标构造出一个有限射影平面，由射影平面与射影平面上一个极性映射导出极性图. 根据 极性图, 对于一些 n，能够构造出 C 4对星 K1,n 的 set Ramsey 数 Ms(C 4, K 1,n) 的极值图。 由此 得到了关于这部分 n 的 Ms(C 4, K 1,n) 的下界并确定了一些新的精确值。
Abstract:A finite projective plane is constructed using parametric coordinates, and a polarity graph is derived from a polarity mapping and the projective plane. For some n, we can construct the extreme graph of set Ramsey numbers for C 4versus stars K1,n according to the polarity graph. The lower bound of Ms( C 4 , K 1,n) is obtained and some new exact values are determined.
文章引用：熊慧芸. 一些关于C 4对星的Set Ramsey 数[J]. 应用数学进展, 2024, 13(2): 869-876. https://doi.org/10.12677/AAM.2024.132082

参考文献

[1] Burger, A.P. and Vuuren, J.H.V. (2004) Ramsey Numbers in Complete Balanced Multipartite Graphs. Part I: Set Numbers. Discrete Mathematics, 283, 37-43.
https://doi.org/10.1016/j.disc.2004.02.004
[2] Magnant, C. and Yusko, A. (2011) Ramsey Set Numbers in Balanced Complete Multipartite Graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, 77, 187.
[3] Goncalves, C.J.F., Carmelo, E.L.M. and Nakaoka, I.N. (2021) Polarity Graphs and C4-Free Multipartite Graphs. Procedia Computer Science, 195, 437-444.
https://doi.org/10.1016/j.procs.2021.11.053
[4] Parsons, T.D. (1976) Graphs from Projective Planes. Aequationes Mathematicae, 14, 167-189.
https://doi.org/10.1007/BF01836217

为你推荐



Baidu
map